Sweeping from the superfluid to Mott phase in the Bose-Hubbard model

TL;DR

This paper analyzes the dynamics of the superfluid to Mott insulator phase transition in the Bose-Hubbard model with a time-dependent tunneling rate, providing analytical insights into fluctuation evolution and order decay during different sweep regimes.

Contribution

It introduces an adapted mean-field approach for large fillings to analytically study the phase transition dynamics under exponential tunneling decay.

Findings

Derived scaling solutions for fluctuations during sweeps

Calculated the decay of off-diagonal long-range order

Described the shrinkage of superfluid fraction in a ring-current setup

Abstract

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate $J(t)$. In the experimentally relevant case of exponential decay, $J(t)\propto e^{-\gamma t}$, an adapted mean-field expansion for large fillings $n$ yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow ($\gamma\ll\mu$), intermediate, and fast (non-adiabatic $\gamma\gg\mu$) sweeps, where $\mu$ is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.